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Algebraic Number Theory
 
 
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Algebraic Number Theory [Paperback]

H. Koch (Author), A.N. Parshin (Editor), I.R. Shafarevich (Editor)

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Book Description

3540630031 978-3540630036 October 16, 1997
From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994
"... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995

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Editorial Reviews

Review

From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995

From the Back Cover

From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences:

"... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes."
Monatshefte fuer Mathematik, 1994
"... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians."
Acta Scientiarum Mathematicarum, 1993

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Inside This Book (learn more)
First Sentence:
The first goal of algebraic number theory is the generalization of the theorem on the unique representation of natural numbers as products of prime numbers to algebraic numbers. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
upper numeration, inessential discriminant divisor, free profinite group, discriminant estimation, dualizing module, divisor theory, finite normal extension, explicit reciprocity law, inertia degree, discriminant theorem, class number formula, idele class group, class field theory, distinguished polynomial, class field tower, wild symbol, general reciprocity law, finite abelian extensions, power residue symbol, profinite groups, convex body theorem, ramification groups, generator rank, maximal real subfield, open normal subgroups
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Artin L-functions, Hecke L-series, Basic Number Theory, Dirichlet L-functions, Hilbert's Satz, Therefore Theorem
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